CHARACTERIZATION OF n-VERTEX GRAPHS WITH METRIC DIMENSION n - 3

For an ordered set W = {w(1)(,) w(2),, w(k)} of vertices and a vertex v in a connected graph G, the ordered k-vector r(v vertical bar W) := (d(v, w(1)), d(v, w(2)),...,d(v,w(k))) is called the metric representation of v with respect to W, where d(x,y) is the distance between vertices x and y. A set W is called a resolving set for G if distinct vertices of G have distinct representations with respect to W. The minimum cardinality of a resolving set for G is its metric dimension. In this paper, we characterize all graphs of order n with metric dimension n 3.